Topology of Spade Drills for Wood Drilling Operations, Part 1: Spade Drill Point Geometry Definition

2005 ◽  
Vol 127 (2) ◽  
pp. 298-309
Author(s):  
Hanxin Zhao ◽  
Kornel F. Ehmann
Keyword(s):  
Mathematical Model ◽  
Construction Industry ◽  
Software Package ◽  
Geometric Analysis ◽  
Analytical Models ◽  
Basic Design ◽  
Technical Literature ◽  
Drilling Operations ◽  
Drill Point ◽  
Geometry And Kinematics

Spade bits, widely and routinely used in the construction industry, have not received any attention in the technical literature, yet there is a pressing need to improve the performance of these bits whose basic design has not changed for decades. To facilitate such improvements, a thorough understanding of the geometric, manufacturing, and cutting mechanics aspects of these tools is necessary. In this two-part paper, the point geometry and manufacturing issues will be discussed. To fundamentally understand the spade drill bit’s behavior, a complete mathematical model of its principal topological elements will be established. In conjunction with this model, the corresponding analytical formulations of the geometry and kinematics of the appropriate manufacturing procedures will also be formulated. In unison, these models will lay the foundation for a methodology and a software package for a detailed geometric analysis of all relevant cutting angle distributions and edge profiles of the spade bit. This will facilitate, at a later point, new point developments rooted in rigorous analytical models.

Topology of Spade Drills for Wood Drilling Operations Part 2: Spade Drill Point Cutting Geometry Analysis

2005 ◽  
Vol 127 (2) ◽  
pp. 310-318
Author(s):  
Hanxin Zhao ◽  
Kornel F. Ehmann
Keyword(s):  
Software Package ◽  
Geometric Model ◽  
Geometric Analysis ◽  
Analysis Procedure ◽  
Angle Distribution ◽  
Cutting Geometry ◽  
Drilling Operations ◽  
Drill Point ◽  
Geometric Elements ◽  
Geometry Analysis

Based on the spade drill point’s mathematical models established in Part 1 of this paper, a detailed methodology for the analysis of the cutting edges and angle distributions along these edges is given. The analysis addresses the most important geometric elements of the bit including the tip, major cutting edge, and the chisel edge profiles, as well as the rake and clearance angle distribution along these cutting edges. In unison, the geometric model of the spade bit and the analysis procedure described in this part of the paper have laid the foundation for a methodology and a software package for a detailed geometric analysis of all relevant cutting mechanics related geometric entities of the drill. This, in turn, constitutes the first prerequisite for assessing the cutting performance of these tools.

scholarly journals Analytical Model of Induction Machines with Multiple Cage Faults Using the Winding Tensor Approach

Sensors ◽  
2021 ◽  
Vol 21 (15) ◽  
pp. 5076
Author(s):  
Javier Martinez-Roman ◽  
Ruben Puche-Panadero ◽  
Angel Sapena-Bano ◽  
Carla Terron-Santiago ◽  
Jordi Burriel-Valencia ◽  
...  
Keyword(s):  
Computational Cost ◽  
Induction Machines ◽  
Diagnostic Techniques ◽  
Analytical Models ◽  
Tensor Algebra ◽  
Diagnostic Systems ◽  
Technical Literature ◽  
Twin Model ◽  
Ring Segment ◽  
The One

Induction machines (IMs) are one of the main sources of mechanical power in many industrial processes, especially squirrel cage IMs (SCIMs), due to their robustness and reliability. Their sudden stoppage due to undetected faults may cause costly production breakdowns. One of the most frequent types of faults are cage faults (bar and end ring segment breakages), especially in motors that directly drive high-inertia loads (such as fans), in motors with frequent starts and stops, and in case of poorly manufactured cage windings. A continuous monitoring of IMs is needed to reduce this risk, integrated in plant-wide condition based maintenance (CBM) systems. Diverse diagnostic techniques have been proposed in the technical literature, either data-based, detecting fault-characteristic perturbations in the data collected from the IM, and model-based, observing the differences between the data collected from the actual IM and from its digital twin model. In both cases, fast and accurate IM models are needed to develop and optimize the fault diagnosis techniques. On the one hand, the finite elements approach can provide highly accurate models, but its computational cost and processing requirements are very high to be used in on-line fault diagnostic systems. On the other hand, analytical models can be much faster, but they can be very complex in case of highly asymmetrical machines, such as IMs with multiple cage faults. In this work, a new method is proposed for the analytical modelling of IMs with asymmetrical cage windings using a tensor based approach, which greatly reduces this complexity by applying routine tensor algebra to obtain the parameters of the faulty IM model from the healthy one. This winding tensor approach is explained theoretically and validated with the diagnosis of a commercial IM with multiple cage faults.

scholarly journals SYNTHESIS OF PROGRAM AND FINITE LAWS OF MOTION IN ANALYTICAL MODELS OF CONTROL OF THE FINAL STATE OF BIOMECHANICAL SYSTEMS

2019 ◽  
Vol 19 (1) ◽  
pp. 93-99
Author(s):  
V Zagrevskiy ◽  
O Zagrevskiy
Keyword(s):  
Mathematical Model ◽  
Computer Program ◽  
Center Of Mass ◽  
Material Point ◽  
Object Motion ◽  
Reference Points ◽  
Analytical Models ◽  
Final State ◽  
Finite Control ◽  
The Mathematical Model

Aim. The article deals with developing a computer program to simulate the movement of the object with a given initial and final speed and fixed travel time. Materials and methods. The analysis, as a method of biomechanics, allows us to assess the biomechanical state of the athlete in real sports exercises. The function of motion synthesis is the ability to predict the trajectory and behavior of the biomechanical system at specified reference points of the phase structure of the simulated motion. The article deals with one of the methods of biomechanical synthesis of movements: synthesis of control of the final state of biomechanical systems, based on the reduction of finite control to a given program control after attenuation of the transient component of acceleration. The mathematical description of the object motion is based on the known law of finite control with feedback. Integration of the mathematical model constructed in the form of the differential equation of the second order was carried out by one of the numerical methods of integration: Runge–Kutta method of the fourth order of accuracy. Consideration of the method is based on a mathematical apparatus describing the motion of a material point, which can be represented by a common center of mass of a biomechanical system, a joint, a center of mass of a segment, etc. Results. The mathematical model of the motion of a material point with the given kinematic parameters of motion at the initial and final moments is implemented in a computer program in the Visual Basic 2010 language environment based on the integrated development environment Visual Studio Express 2013. The output provides numerical and visual support for simulation results. Conclusion. It is shown that the developed computer model of the method always implements the goal of motion: to transfer an object from a given initial state by speed to a given final state for a fixed time of movement.

scholarly journals Identification of Neural Network Model of Robot to Solve the Optimal Control Problem

2021 ◽  
Vol 20 (6) ◽  
pp. 1254-1278
Author(s):  
Elizaveta Shmalko ◽  
Yuri Rumyantsev ◽  
Ruslan Baynazarov ◽  
Konstantin Yamshanov
Keyword(s):  
Neural Network ◽  
Machine Learning ◽  
Mathematical Model ◽  
Optimal Control ◽  
Neural Network Model ◽  
Software Package ◽  
Control Object ◽  
Robotic Systems ◽  
Object Model ◽  
Modern Machine

To calculate the optimal control, a satisfactory mathematical model of the control object is required. Further, when implementing the calculated controls on a real object, the same model can be used in robot navigation to predict its position and correct sensor data, therefore, it is important that the model adequately reflects the dynamics of the object. Model derivation is often time-consuming and sometimes even impossible using traditional methods. In view of the increasing diversity and extremely complex nature of control objects, including the variety of modern robotic systems, the identification problem is becoming increasingly important, which allows you to build a mathematical model of the control object, having input and output data about the system. The identification of a nonlinear system is of particular interest, since most real systems have nonlinear dynamics. And if earlier the identification of the system model consisted in the selection of the optimal parameters for the selected structure, then the emergence of modern machine learning methods opens up broader prospects and allows you to automate the identification process itself. In this paper, a wheeled robot with a differential drive in the Gazebo simulation environment, which is currently the most popular software package for the development and simulation of robotic systems, is considered as a control object. The mathematical model of the robot is unknown in advance. The main problem is that the existing mathematical models do not correspond to the real dynamics of the robot in the simulator. The paper considers the solution to the problem of identifying a mathematical model of a control object using machine learning technique of the neural networks. A new mixed approach is proposed. It is based on the use of well-known simple models of the object and identification of unaccounted dynamic properties of the object using a neural network based on a training sample. To generate training data, a software package was written that automates the collection process using two ROS nodes. To train the neural network, the PyTorch framework was used and an open source software package was created. Further, the identified object model is used to calculate the optimal control. The results of the computational experiment demonstrate the adequacy and performance of the resulting model. The presented approach based on a combination of a well-known mathematical model and an additional identified neural network model allows using the advantages of the accumulated physical apparatus and increasing its efficiency and accuracy through the use of modern machine learning tools.

Research for Tool Face Mathematical Model of Multi-Facet Drills Used in Processing High Manganese Steel

2011 ◽  
Vol 299-300 ◽  
pp. 936-939
Author(s):  
Li Xu ◽  
Liang Yang ◽  
Zhi Hui Shi
Keyword(s):  
Mathematical Model ◽  
Manganese Steel ◽  
Design Parameters ◽  
High Manganese ◽  
High Manganese Steel ◽  
Drilling Tool ◽  
Grinding Method ◽  
Grinding Parameters ◽  
New Type ◽  
Drill Point

The multi-facet drill shows good performance during materials are difficultly machined. However, for a new type of the drilling point, the grinding has been the main problem that restricts its application. To properly grinding the drill point confirms the design parameters, the relationship between design parameters and grinding parameters must be resolved. The mathematical model is the key to solve this problem. In this paper, according to the design of the high manganese steel drilling tool, a mathematical model has been established by the plane grinding method to solve grinding parameters, and to achieve improved mechanical grinding of drill point.

scholarly journals Shear strength analysis of slabs without transverse reinforcement under concentrated loads according to ABNT NBR 6118:2014

2019 ◽  
Vol 12 (3) ◽  
pp. 658-693
Author(s):  
A. M. D. SOUSA ◽  
M. K. EL DEBS
Keyword(s):  
Shear Strength ◽  
Shear Force ◽  
Highway Bridges ◽  
Analytical Models ◽  
Strength Analysis ◽  
Transverse Reinforcement ◽  
Concentrated Loads ◽  
Technical Literature ◽  
Experimental Database ◽  
Small Areas

Abstract Concentrated loads in slabs without transverse reinforcement, usual in highway bridges, result in the horizontal spreading of the shear force towards the supports, situation in which not all the slab width contributes in the shear strength. Based on this, the analytical models of shear strength and punching capacity in slabs may not be suitable to deal with this loading. Since this topic is not widely discussed in the national technical literature, the paper aims to present contributions to these analyses with a focus on the accuracy level of the shear strength analytical models recommended by ABNT NBR 6118:2014. Therefore, the models available in the Brazilian code were applied to an experimental database with 118 test results and the results obtained by the Brazilian and European codes were compared. The results demonstrated that, as presented in the Brazilian code, shear strength model in one-way slabs can lead to unsafe resistance predictions while the punching capacity model can lead to very conservative predictions. From the analysis, it is concluded that considering the reduction of the shear force, in the case of loads distributed in small areas close to the support in slabs, and the use of more suitable procedures to define the effective width, it is possible to improve the level of accuracy of relations between experimental and theoretical values, but this still leads to high percentages of unsafe predictions of resistance (> 40%).

STUDY OF A SINGLE SCREW COMPRESSOR WITH A CONICAL TEETH GATE ROTOR

2008 ◽  
Vol 32 (3-4) ◽  
pp. 333-352
Author(s):  
Yang Shyue-Cheng ◽  
Tsang-Lang Liang
Keyword(s):  
Mathematical Model ◽  
Mathematical Models ◽  
Software Package ◽  
Analytical Procedure ◽  
Conjugate Problem ◽  
Screw Compressor ◽  
Main Rotor ◽  
Conjugate Pair ◽  
Single Screw ◽  
Envelope Theory

From a geometric viewpoint, a mathematical model of a single screw compressor with a conjugate pair of meshing conical teeth gate rotor is a conjugate problem. Coordinate transformation and envelope theory are applied to determine the sets of spatial points of the contacting surfaces that define the main rotor of a single screw compressor. Envelope theory and analytical procedure are used to derive mathematical models of a gate rotor and a main rotor. Stress analysis for the single screw compressor mechanism is performed. PowerMILL software package is used to simulate the manufacture of a main rotor. A numerical example with a compressor ratio of 11:6 is presented to demonstrate the application of the mathematical models developed in this paper.

Wildhaber–Novikov circular arc gears: some properties of relevance to their design

1989 ◽  
Vol 425 (1869) ◽  
pp. 341-363 ◽  
Keyword(s):  
Contact Stress ◽  
Contact Area ◽  
Entire Range ◽  
Basic Theory ◽  
Helicopter Rotor ◽  
Basic Design ◽  
Circular Arc ◽  
Pressure Angle ◽  
Final Drive ◽  
Geometry And Kinematics

This paper follows an earlier one by Dyson et al. (Proc. R. Soc. Lond . A 403, 313 (1986)) in which a rigorous basic theory of the geometry and kinematics of Wildhaber–Novikov circular arc gears was developed. It was then applied to a pair of helicopter rotor final drive gears, operating in the conditions for which they were designed. The present paper extends this treatment by considering the effect of some variations on the same basic design, and of operating in conditions different from those for which the gears were designed. Aspects considered include the sensitivity of the pressure angle to changes in centres distance, the compromise between this sensitivity and reduction in contact stress, the relation between pressure angle and centres distance over the entire range theoretically possible, the avoidance of interference, the extent of the contact area in terms of position on the teeth, backlash and internal gears.

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